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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/99611


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/99611


    Title: The Existence of (s,t)-Monochromatic-rectangles in a 2-colored Checkerboard
    Authors: 卓駿焰
    Contributors: 張宜武
    卓駿焰
    Keywords: 完全二分圖
    單色子圖
    Date: 2016
    Abstract: 本文藉由矩形棋盤著色探討完全二分圖K_{m,n}由兩種顏色任意塗邊，使得此兩色著邊之完全二分圖$K_{m,n}$會包含單色子圖K_{s,2}、K_{s,3}與K_{s,t} （s大於或等於 2），我們將討論參數n與s之間滿必須滿足何種關係。
    本文也將介紹處理棋盤著色問題的一般方法與技巧，以及透過棋盤如何將棋盤問題轉化為圖論問題，並且將它推廣。
    Reference: [1] Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer. Ramsey theory. Wiley Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., Hoboken, NJ, 2013.
    [2] Douglas B. West. Introduction to graph theory. Prentice Hall, Inc., Upper Saddle River, NJ, 1996.
    [3] 李炯生. 棋盤染色問題與二部 Ramsey 數. 數學, 21(3):63–72, 9 月 1997.
    [4] 林子軒. The coloring of a checkerboard and the monochromatic subgraphs of a complete bipartite graph. 國立政治大學應用數學系碩士學位論文, 2013.
    Description: 碩士
    國立政治大學
    應用數學系
    102751001
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0102751001
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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